EP4720907A1 - Method for modeling road-tire interaction - Google Patents

Abstract

A computer system (100) comprising processing circuitry (102) is provided. The processing circuitry is configured to retrieve (61) a modeled vehicle tire (3') from a tire model (10), determine (62) a plurality of grid points (41a-c, 42a-c, 43a-c) of the modeled vehicle tire (3'), said grid points (41a-c, 42a-c, 43a-c) being distributed in a lateral and longitudinal direction of the modeled vehicle tire (3'), retrieve (63) a modeled road (5') from a road model (20), determine (64) a plurality of projected grid points (51a-c, 52a-c, 53a-c) of the modeled road (5') by projecting each of the grid points (41a-c, 42a-c, 43a-c) of the modeled vehicle tire (3') on the modeled road, determine (65) a continuous road surface segment from the projected grid points (51a-c, 52a-c, 53a-c), and compute (66) at least one road-tire interaction parameter (RTIP) from the continuous road surface segment.

Description

METHOD FOR MODELING ROAD-TIRE INTERACTION

TECHNICAL FIELD

[1] The disclosure relates generally to modeling road-tire interaction. In particular aspects, the disclosure relates to a computer-implemented method and a computer system comprising processing circuitry configured to modeling road-tire interaction for a vehicle. The disclosure can be applied to heavy-duty vehicles, such as trucks, buses, and construction equipment, among other vehicle types. Although the disclosure may be described with respect to a particular vehicle, the disclosure is not restricted to any particular vehicle.

BACKGROUND

[2] In vehicle dynamics the road-tire interaction is of great importance. Modeling of the road-tire interaction is particularly performed in order to determine the dynamics of how a vehicle tire interacts with the road surface. Accurate modeling of the road-tire interaction is critical in order to provide the desired control of various vehicle sub-systems, thereby improving vehicle performance, vehicle safety, and vehicle operation.

[3] When data concerning the road and the tire are provided by different simulation models, the road-tire interaction may be simulated using a technique called co-simulation. This means that the complex interaction between the tire and the ground is simulated by an integration of a vehicle model and a ground model. Typically, in co-simulation of the roadtire interaction the vehicle model runs in a dedicated simulation environment while the ground model runs in another dedicated simulation environment.

[4] The outputs of the different simulation environments are combined to co-simulate the road-tire interaction, potentially allowing for a more detailed and accurate modeling of the road-tire interaction in order to deal with complex situations, such as the effects of road surface changes on the vehicle's handling and stability.

[5] While the road-tire interaction may be accurately modeled by co-simulation on flat and even grounds, problems have been identified when the ground normal deviates from an entirely vertical direction and/or when the ground is uneven. In multi-domain non-iterative co-simulation, the information exchange on physical interfaces (i.e. where the interaction between different objects is governed by physics and first principles) is very tricky because physics is continuous. In multi-domain non-iterative co-simulation including vehicle models, this often boils down to the interaction between the tires and the ground, where the simulation platform is responsible for the communication and information (i.e. change in position) exchange between the vehicle model and the ground model.

[6] While on a computer system the information exchange between tire and ground is discrete and limited by the time step of the communication interval, one must ensure that conservation of energy is maintained in the continuous vehicle model. This is not a trivial task. Introducing discrete changes in positions from the ground model entails introducing infinite forces and energy into a physics system (i.e. the vehicle model), which renders the results of simulation meaningless and possibly causes the model solver to crash. As one practical example, errors in simulating road-tire interaction may lead to a vehicle starting to move when intended to stand still in a slope, even if the ground surface is perfectly flat.

[7] Another aspect to consider is simulation speed. The well-known simplified point follower tire model, which allows for fast simulation times because of its simplicity, suffers from the problem mentioned above.

[8] Based on the above limitations of the available approaches to modeling the roadtire interaction, there is a need for improvements.

SUMMARY

[9] According to a first aspect of the disclosure, a computer system is provided. The computer system comprises processing circuitry configured to: retrieve a modeled vehicle tire from a tire model, determine a plurality of grid points of the modeled vehicle tire, said grid points being distributed in a lateral and longitudinal direction of the modeled vehicle tire, retrieve a modeled road from a road model, determine a plurality of projected grid points of the modeled road by projecting each of the grid points of the modeled vehicle tire on the modeled road, determine a continuous road surface segment from the projected grid points, and compute at least one road-tire interaction parameter from the continuous road surface segment. The first aspect of the disclosure may seek to improve co-simulation of road-tire interface, especially on even ground. A technical benefit may include filtering the ground shape to ensure a continuous tire-ground contact.

[10] Projecting each of the grid points of the modeled vehicle tire on the modeled road may be performed by finding the position where a line, extending from a grid point, intersects with a surface of the modeled road. Preferably the line may be vertical, whereby the projected grid point corresponds to the horizontal position where the vertical line intersects with the modeled road surface segment.

[11] Optionally, in some examples, the tire model is a continuous tire model and/or the modeled vehicle tire is a continuous representation of the vehicle tire.

[12] Optionally in some examples, including in at least one preferred example, the processing circuitry is further configured to: update the at least one road-tire interaction parameter by continuously repeating retrieve the modelled vehicle tire, determine the plurality of grid points of the modelled vehicle tire, retrieve the modelled road, determine the plurality of projected grid points, determine the continuous road surface segment, and compute at least one road-tire interaction parameter from the continuous road surface segment. A technical benefit may include continuous co-simulation of road-tire interaction, thereby supporting efficient variable step-solvers. Especially, in native simulations the road normal may change discrete, because the road profile is only continuous in zeroth derivative while it is discontinuous in the first derivative. To the contrary, the disclosed examples will filter this and create a virtual continuous road surface segment to the second order.

[13] Optionally in some examples, including in at least one preferred example, the processing circuitry is further configured to: adjusting the longitudinal distribution of the plurality of grid points of the modelled vehicle tire when updating the at least one road-tire interaction parameter. A technical benefit may include adapting the resolution of the continuous road surface segment in order to improve accuracy of the ground shape.

[14] Optionally in some examples, including in at least one preferred example, the processing circuitry is further configured to: compress the longitudinal distribution of the plurality of grid points of the modelled vehicle tire when updating the at least one road-tire interaction parameter. A technical benefit may include increasing the resolution of the ground shape.

[15] Optionally in some examples, including in at least one preferred example, the processing circuitry is further configured to: assign at least one of the projected grid points as an actual contact point, and to compute the continuous road surface segment to include the immediately preceding at least one actual contact point. A technical benefit may include ensuring a continuous tire-road contact. [16] Optionally in some examples, including in at least one preferred example, the at least one road-tire interaction parameter is a road normal. A technical benefit may include obtaining a usable parameter for vehicle dynamics and control.

[17] Optionally in some examples, including in at least one preferred example, the processing circuitry is further configured to: determine the plurality of grid points as a nxn grid, preferably n equals 3. A technical benefit may include an efficient optimization of accuracy in relation to computing power.

[18] Optionally in some examples, including in at least one preferred example, the processing circuitry is further configured to determine the continuous road surface segment by defining a n-dimensional quadratic equation. A technical benefit may include removing the discontinuous inputs of traditionally point-follower tire-road interactions on discretized surfaces.

[19] Optionally in some examples, including in at least one preferred example, the processing circuitry is further configured to compute the at least one road-tire interaction parameter from at least one partial derivative of the n-dimensional quadratic equation. A technical benefit may include using efficient analytical tools on the filtered ground shape.

[20] Optionally in some examples, including in at least one preferred example, the processing circuitry is further configured to determine longitudinally distributed parallel sets of grid points of the modeled vehicle tire, wherein each set of grid points extends laterally. A technical benefit may include optimization of estimating the ground shape across the entire lateral extension of the tire.

[21] Optionally in some examples, including in at least one preferred example, the processing circuitry is further configured to: determine a rearward set of grid points at the center of a contact patch of the tire. A technical benefit may include estimating the ground shape in contact with the tire.

[22] Optionally in some examples, including in at least one preferred example, the processing circuitry is further configured to: determine a center set of grid points in front of a contact patch of the tire. A technical benefit may include estimating the ground shape immediately ahead of the contact patch of the tire.

[23] Optionally in some examples, including in at least one preferred example, the processing circuitry is further configured to: determine a forward set of grid points at the front position of the tire. A technical benefit may include estimating the ground shape further ahead of the contact patch of the tire.

[24] Optionally in some examples, including in at least one preferred example, the at least one road-tire interaction parameter is a road normal, and the processing circuitry is further configured to: determine the plurality of grid points as a nxn grid, update the at least one road-tire interaction parameter by continuously repeating retrieve the modelled vehicle tire, determine the plurality of grid points of the modelled vehicle tire, retrieve the modelled road, determine the plurality of projected grid points, determine the continuous road surface segment, and compute at least one road-tire interaction parameter from the continuous road surface segment. The processing circuitry is further configured to compress the longitudinal distribution of the plurality of grid points of the modelled vehicle tire when updating the at least one road-tire interaction parameter, assign at least one of the projected grid points as an actual contact point, and to compute the continuous road surface segment to include the immediately preceding at least one actual contact point. The processing circuitry is further configured to determine the continuous road surface segment by defining a n-dimensional quadratic equation, compute the at least one road-tire interaction parameter from at least one partial derivative of the n-dimensional quadratic equation, determine longitudinally distributed parallel sets of grid points of the modeled vehicle tire, wherein each set of grid points extends laterally, and to determine a rearward set of grid points at the center of a contact patch of the tire, a center set of grid points in front of a contact patch of the tire, and a forward set of grid points at the front position of the tire.

[25] According to a second aspect, a vehicle is provided. The vehicle comprises the computer system of the first aspect.

[26] According to a third aspect, a computer-implemented method is provided. The computer-implemented method comprises: retrieving , by processing circuitry of a computer system, a modeled vehicle tire from a tire model, determining, by the processing circuitry, a plurality of grid points of the modeled vehicle tire, said grid points being distributed in a lateral and longitudinal direction of the modeled vehicle tire, retrieving, by the processing circuitry, a modeled road from a road model, determining, by the processing circuitry, a plurality of projected grid points of the modeled road by projecting each of the grid points of the modeled vehicle tire on the modeled road, determining, by the processing circuitry, a continuous road surface segment from the projected grid points, and computing, by the processing circuitry, at least one road-tire interaction parameter from the continuous road surface segment.

[27] Optionally in some examples, including in at least one preferred example, the at least one road-tire interaction parameter is a road normal. A technical benefit may include obtaining a usable parameter for vehicle dynamics and control.

[28] Optionally in some examples, including in at least one preferred example, retrieving a modeled vehicle tire, determining a plurality of grid points of the modeled vehicle tire, retrieving a modeled road, determining a plurality of projected grid points of the modeled road, determining a continuous road surface segment, and computing at least one road-tire interaction parameter, is performed for each one of a plurality of wheels of a vehicle. According to a fourth aspect, a computer program product is provided. The computer program product comprises program code for performing, when executed by the processing circuitry, the method of the third aspect.

[29] According to a fifth aspect, a non-transitory computer-readable storage medium is provided. The non-transitory computer-readable storage medium comprises instructions, which when executed by the processing circuitry, cause the processing circuitry to perform the method of the third aspect.

[30] The disclosed aspects, examples (including any preferred examples), and/or accompanying claims may be suitably combined with each other as would be apparent to anyone of ordinary skill in the art. Additional features and advantages are disclosed in the following description, claims, and drawings, and in part will be readily apparent therefrom to those skilled in the art or recognized by practicing the disclosure as described herein.

[31] There are also disclosed herein computer systems, control units, code modules, computer-implemented methods, computer readable media, and computer program products associated with the above discussed technical benefits.

BRIEF DESCRIPTION OF THE DRAWINGS

[32] Examples are described in more detail below with reference to the appended drawings.

[33] FIG. 1 is an exemplary isometric view of a vehicle according to an example.

[34] FIG. 2 is a schematic diagram of a computer system according to an example.

[35] FIG. 3A is an exemplary side view of a vehicle tire according to an example.

RECTIFIED SHEET (RULE 91) ISA/EP [36] FIG. 3B is an isometric view of the vehicle tire shown in FIG. 3A.

[37] FIG. 4 is an exemplary view of the selection of grid points for a vehicle tire according to an example.

[38] FIG. 5 is an exemplary side view of the road-tire interaction according to an example.

[39] FIG. 6A is an exemplary diagram of the ground represented by projected grid points according to an example.

[40] FIG. 6B is an exemplary diagram of the ground represented by a continuous surface interpolated from the projected grid points shown in FIG. 6A.

[41] FIGS. 7A-J are exemplary diagrams of the ground represented by continuous surfaces interpolated from consecutive projected grid points as a vehicle travels.

[42] FIG. 8 is an exemplary diagram of a computer-implemented method for modelling road-tire interaction according to an example.

[43] FIG. 9 is an exemplary diagram of a computer-implemented method for modelling road-tire interaction according to an example.

[44] FIG. 10 is a schematic diagram of an exemplary computer system for implementing examples disclosed herein, according to an example.

DETAILED DESCRIPTION

[45] The detailed description set forth below provides information and examples of the disclosed technology with sufficient detail to enable those skilled in the art to practice the disclosure.

[46] FIG. 1 is an exemplary system diagram of a vehicle 1 according to an example. The vehicle 1, although illustrated as being in the form of a truck, may be any type of vehicle, such as a heavy duty vehicle or a light duty vehicle. The vehicle 1 comprises a plurality of tires 3 interacting with the underlying ground or road 5. A computer system 100 is associated with the vehicle 1 and configured to model the interaction between one or more tires 3 and the road 5. In FIG. 1, the computer system 100 is an on-board system however an off-board computer system 100 is also possible as well as any combination of on-board and off-board computer systems 100.

[47] FIG. 2 is an exemplary diagram of a computer system 100 implemented to cosimulate the interaction between the road and the tire of the vehicle. The computer system 100 thus forms a simulation platform being responsible for the communication and information exchange between a tire model 10 and a road model 20.

[48] The tire model 10 may be any suitable software or hardware implemented model capable of communicating data representing one or more modelled or estimated physical parameter of a vehicle tire 3. The tire model 10 may for example comprise one or more sensors 12 and/or other data providing algorithms or circuitry 14. Input data is received by a simulation software 16 configured to determine the one or more physical parameter of the vehicle tire 3 based on various input data, such as from the sensor(s) 12 and/or the data providing algorithms or circuitry 14.

[49] Similarly, the ground model 20 may be any suitable software or hardware implemented model capable of communicating data representing one or more modelled or estimated physical parameter of the ground 5 beneath and ahead of the vehicle tire 3. The ground model 20 may for example comprise one or more sensors 22 and/or other data providing algorithms or circuitry 24 such as GPS, LIDAR, cameras, etc. Input data is received by a simulation software 26 configured to determine the one or more physical parameter of the ground 5 based on various input data, such as from the sensor(s) 22 and/or the data providing algorithms or circuitry 24.

[50] The computer system 100 comprises processing circuitry 102 being configured to receive input from the tire model 10 and from the road model 20 in order to determine a roadtire interaction parameter RTIP. The road-tire interaction parameter, which for example may be the road normal, may be communicated to a further vehicle model 30.

[51] The processing circuitry 102 comprises a first input receiving circuitry 130 being configured to retrieve a modeled vehicle tire, which may or may not be continuous, from the tire model 10, and an assignment circuitry 132 configured to determine a plurality of grid points of the modeled vehicle tire 3. The determined grid points are distributed in a lateral and longitudinal direction of the modeled vehicle tire 3. The plurality of grid points may be determined as a plurality of parallel sets of grid points of the modelled vehicle tire 3. Each parallel set of grid points may extend laterally, i.e. at a cross-wise direction in relation to the forward direction of the vehicle tire 3. Preferably, the assignment circuitry is programmed to determine the plurality of grid points as a nxn grid. The number n may be selected as any suitable integer. According to one example, the plurality of grid points is determined as a 3x3 grid. Such 3x3 grid may be determined as a rearward set of grid points at the center of a contact patch of the tire 3, a center set of grid points in front of the contact patch of the tire 3, and a forward set of grid points at the front position of the tire 3.

[52] The processing circuitry 102 further comprises a second input receiving circuitry 140 being configured to retrieve a modeled road from the road model 20, and a determining circuitry 142 configured to determine a plurality of projected grid points of the modeled road 5. The projected grid points are determined by projecting a ray cast from each of the grid points of the modeled vehicle tire 3. At least one projected grid point may be assigned as the actual contact point between the road 5 and the tire 3.

[53] The processing circuitry 102 further comprises interpolation circuitry 150 configured to determine a continuous road surface segment from the projected grid points, and computing circuitry 160 configured to compute at least one road-tire interaction parameter from the continuous road surface segment.

[54] The interpolation circuitry 150 is preferably configured to define a three- dimensional quadratic equation from the projected grid points. According to one example, the interpolation circuitry 150 is configured to include a projected grid point representing an immediately preceding contact point between the tire 3 and the road 5, when interpolating the quadratic equation from the current projected grid points.

[55] The computing circuitry 160 may, according to one example, be configured to compute the at least one road-tire interaction parameter by computing a partial derivative of the three-dimensional quadratic equation. The at least one road-tire interaction parameter may for example be the road normal.

[56] During execution, the processing circuitry 102 is preferably configured to continuously update the computed road-tire interaction parameter. This may be done by receiving updated models of the tire 3 and/or road 5, and subsequent operation of the assignment circuitry 132, determining circuitry 142, interpolation circuitry 150, and computing circuitry 160.

[57] According to one example, the distribution of the plurality of grid points may be dynamically altered, meaning that the assignment circuitry 134 is configured to determine the positions of the grid points based on some pre-set criteria. For example, the assignment circuitry 134 may assign the grid points according to an extended distribution, and in a next run the assignment circuitry 134 may assign the grid points according to a compressed distribution. [58] FIGS. 3A and 3B show a vehicle tire 3 and in particular how grid points 40 may be selected according to one example. The tire 3 is in contact with a road 5, defining a contact patch 7. When receiving the tire model, the assignment circuitry 134 determines a set of grid points 40. In the shown example, illustrated by FIGS. 3A and 3B, the grid points 40 are determined as a 3x3 grid comprising three laterally spaced grid points 41a-c arranged at the center of the contact patch 7, three laterally spaced grid points 42a-c arranged immediately in front of the contact patch 7, and three laterally spaced grid points 43a-c arranged at the frontmost position of the tire 3. Preferably, the lateral extension is selected to cover the entire width, or at least the majority of the width of the tire 3.

[59] From the set of grid points 40 a set of projected grid points 50 is determined. Hence, each grid point 41a-c, 42a-c, 43a-c will be associated with a corresponding projected grid point 51a-c, 52a-c, 53a-c as specifically shown in FIG. 4.

[60] In one example, each projected grid point 51a-c, 52a-c, 53a-c is determined by projecting a vertical line from the grid point 41a-c, 42a-c, 43a-c downward in the vertical direction, as illustrated by the vertical arrows in FIG. 3A. The projected grid point 51a-c, 52a-c, 53a-c will then correspond to a point where the line intersects with the modeled road.

[61] In another example, each grid point 41a-c, 42a-c, 43a-c is on the center of the wheel hub of the tire 3, whereby each projected grid point 51a-c, 52a-c, 53a-c is determined by projecting a line radially out from the grid point 41a-c, 42a-c, 43a-c in order to find the closest road contact.

[62] The principle of projected grid points is shown in FIG. 4. Each grid point 41a-c, 42a-c, 43a-c of the tire 3 is projected vertically downwards to form an associated projected grid point 51a-c, 52a-c, 53a-c on the road 5. As mentioned above, the projected grid point 51a-c, 52a-c, 53a-c is positioned where the line, extending from the grid point 41a-c, 42a-c, 43a-c, intersects with the surface of the modeled road.

[63] In FIG. 5 a running tire 3 is illustrated, travelling along a road 5 with a small object 9 in the forward direction F as indicated by the arrow. The object 9 is present in the road model forming input to the co-simulation procedure. When the object 9 is located at the same longitudinal position as the front of the tire 3, the object 9 will define the closest point of contact for the foremost grid points on the tire 3. Hence, the resulting interpolated curve will look as illustrated in the diagram of FIG. 5 underneath the tire 3, i.e. as a smooth uphill inclination. [64] At a subsequent time step of the co-simulation procedure, the object 9 will be arranged longitudinally in between two projected grid points, i.e. between the foremost and central grid points. Consequently, the object 9 will not contribute to the resulting interpolated curve which will be entirely flat, as indicated in the diagram of FIG. 5.

[65] At a yet subsequent time step of the co-simulation procedure, the object 9 will be arranged longitudinally aligned with the central grid point. Consequently, the object 9 will in this situation do contribute to the resulting interpolated curve which will have a local maximum, as indicated in the diagram of FIG. 5.

[66] The situation described with reference to FIG. 5 relates to spatial filtering, i.e. what spatial frequency being allowed and of interest. In FIG. 5, the object 9 has a higher spatial frequency (i.e. being smaller) than the chosen grid, which means that the object 9 will act as a disturbance to the tire model. In such case the road contact will be continuous, but spatial aliases may occur.

[67] An example of a curve fitting procedure of the road 5 is shown in FIGS. 6A and 6B. Starting in FIG. 6A, nine projected grid points 51a-c, 52a-c, 53a-c are shown in a space diagram. From these projected grid points 51a-c, 52a-c, 53a-c the road surface segment is interpolated to a smooth three-dimensional quadratic equation, as shown in FIG. 6B.

[68] In FIGS. 7A-J a time series of co-simulated road surface segment is shown. In FIGS. 7A-C the modelled road surface segment is smooth and planar, while in FIG. 7D the front area of the tire is modeled to face an uphill portion of the road. In FIGS. 7E-F the entire tire has travelled along the uphill portion, which according to the model is rather a local bump in the road. In FIG. 7G the tire is facing a downhill portion, indicating the end of the local bump. In FIG. 7H the tire has almost travelled past the local bump, which is further indicated in FIGS. 7I-J indicating the road surface segment again as flat.

[69] FIG. 8 is a schematic diagram of a computer-implemented method 60 being designed to model, or co-simulate, road-tire interaction of a vehicle.

[70] The method 60 is performed by retrieving 61, by processing circuitry 102 of a computer system 100, a modeled vehicle tire 3’ from a tire model 10. The method 60 is further performed by determining 62, by the processing circuitry 102, a plurality of grid points 41a-c, 42a-c, 43a-c of the modeled vehicle tire 3’. The grid points 41a-c, 42a-c, 43a-c are preferably distributed in a lateral and longitudinal direction of the modeled vehicle tire 3’. [71] In one example, the method 60 determines 62 the plurality of grid points 41a-c, 42a-c, 43a-c as a nxn grid, wherein n may be selected as the number 3.

[72] The plurality of grid points 41a-c, 42a-c, 43a-c may be determined 62 as longitudinally distributed parallel sets of grid points of the modelled vehicle tire 3, wherein each set of grid points extends laterally across the tire 3 width. A rearward set of grid points may be arranged at the center of a contact patch of the tire 3, and a central set of grid points may be arranged in front of the contact patch. A foremost set of grid points may be arranged at the front position of the tire 3.

[73] The method 60 also comprises retrieving 63, by the processing circuitry 102 of a computer system 100, a modeled road 5’ from a road model 20.

[74] From the modeled road 5’ and the determined grid points 41a-c, 42a-c, 43a-c of the modeled vehicle tire 3’ the method 60 is further configured to determine 64, by the processing circuitry 102, a plurality of projected grid points 51a-c, 52a-c, 53a-c of the modeled road 5’. The plurality of projected grid points 51a-c, 52a-c, 53a-c may for example be determined 64 by projecting a vertical ray cast from each of the grid points 41a-c, 42a-c, 43a-c of the modeled vehicle tire 3’ however other ways for projecting grid points are also possible, as explained earlier.

[75] From the plurality of projected grid points 51a-c, 52a-c, 53a-c the method 60 is configured to determine 65, by the processing circuitry 102, a continuous road surface segment.

[76] The method 60 is further configured to compute 66, by the processing circuitry 102, at least one road-tire interaction parameter, such as a road normal, from the continuous road surface segment.

[77] As illustrated in FIG. 8, the method 60 is repeated continuously in order to provide regular time-step updates of the at least one road-tire interaction parameter. Also, while the method 60 is illustrated for a single tire 3 only, it should be noted that the method 60 may be performed in parallel for a plurality of tires 3, such as each tire 3, of an associated vehicle 1.

[78] Upon determining 62 the plurality of grid points 41a-c, 42a-c, 43a-c of the modeled vehicle tire 3’ the method 60 may be configured to adjusting 67 the longitudinal distribution of the plurality of grid points 41a-c, 42a-c, 43a-c, in particular when the method 60 is repeated to update the at least one road-tire interaction parameter. Adjusting 67 the longitudinal distribution of the plurality of grid points 41a-c, 42a-c, 43a-c may be performed by expanding or compressing the longitudinal distribution.

[79] The method 60 may further comprise, after determining 64 the projected grid points 51a-c, 52a-c, 53a-c, assign 68 at least one of the projected grid points 51a-c, 52a-c, 53a-c as an actual contact point. Upon such assignment, computing 65 the continuous road surface segment is preferably performed by including the immediately preceding at least one actual contact point.

[80] Determining 65 the continuous road surface segment may preferably be performed by defining 69 a three-dimensional quadratic equation from the projected grid points 51a-c, 52a-c, 53a-c. For such example, computing 66 the at least one road-tire interaction parameter is preferably performed by computing 70 a partial derivative of the three-dimensional quadratic equation.

[81] FIG. 9 is another schematic diagram of a computer-implemented method 60 being designed to model, or co-simulate, road-tire interaction of a vehicle.

[82] The method 60 is performed by retrieving 61, by processing circuitry 102 of a computer system 100, a modeled vehicle tire 3’ from a tire model 10. The method 60 is further performed by determining 62, by the processing circuitry 102, a plurality of grid points 41a-c, 42a-c, 43a-c of the modeled vehicle tire 3’. The grid points 41a-c, 42a-c, 43a-c are preferably distributed in a lateral and longitudinal direction of the modeled vehicle tire 3’.

[83] In one example, the method 60 determines the plurality of grid points 41a-c, 42a- c, 43a-c as a nxn grid, wherein n may be selected as the number 3.

[84] The method 60 also comprises retrieving 63, by the processing circuitry 102 of a computer system 100, a modeled road 5’ from a road model 20.

[85] From the modeled road 5’ and the determined grid points 41a-c, 42a-c, 43a-c of the modeled vehicle tire 3’ the method 60 is further configured to determine 64, by the processing circuitry 102, a plurality of projected grid points 51a-c, 52a-c, 53a-c of the modeled road 5’. The plurality of projected grid points 51a-c, 52a-c, 53a-c may for example be determined 64 by projecting a vertical ray cast from each of the grid points 41a-c, 42a-c, 43a-c of the modeled vehicle tire 3’ however other ways for projecting grid points are also possible, as explained earlier. [86] From the plurality of projected grid points 51a-c, 52a-c, 53a-c the method 60 is configured to determine 65, by the processing circuitry 102, a continuous road surface segment.

[87] The method 60 is further configured to compute 66, by the processing circuitry 102, at least one road-tire interaction parameter, such as a road normal, from the continuous road surface segment.

[88] From the above, a method and system has been described which improves current techniques by determining a three-dimensional quadratic equation fitted to projected ground points, being closest to the tire 3 wheel at a specified location. This provides for a simplified ground estimation for faster than real-time performance in order to solve the point follower problems on non-flat surfaces. Further, the continuously updated ground estimation supports efficient variable step solvers. Another advantageous feature is that the interaction parameter, i.e. the road normal, is computed analytically from partial derivatives in the Cartesian coordinates. This approach removes the discontinuous inputs of traditional point-follower tire-road interactions on discretized surfaces, which is known to be a common problem in multi-body simulation solutions.

[89] The above described solution do not only improve solver performance, but also targets model robustness. Ensuring a smooth ground means eliminating the risk for infinite energy input into the system, which inherently improves the robustness of simulations.

[90] The spatial permissible bandwidth is normally a function of the size of the nine- point estimated surface. It is thus possible to have high granularity of road descriptions, but it would require smaller nine-point surfaces.

[91] When selecting the number of grid points and their longitudinal distribution, it is noted that a 3x3 is efficient to lead to a second order spatial filter. 3x3 grid size also has a regression value R=1 result from the linear solution p=A\z which means that the actual contact point is always exactly matched, which has proven to be an advantageous aspect of smooth and sound simulation results. 3x3 grid size also guarantees the Oth and 1st order to be continuous as long as the actual contact point is one of the nine points.

[92] Spatial filtering has proven to allow for sampled time from co-simulations and still have continuous road profiles during the continuous time integration schemes in between the samples. This solution can benefit all tire-road simulation. The use of a nine-point estimate second order surface on the point-follower contact point will be continuous in the 0- th and 1-st order. This improves simulation performance by filtering the high-frequency disturbances caused by discontinuous O-th and 1-st order of the contact point.

[93] FIG. 10 is a schematic diagram of a computer system 100 for implementing examples disclosed herein. The computer system 100 is adapted to execute instructions from a computer-readable medium to perform these and/or any of the functions or processing described herein. The computer system 100 may be connected (e.g., networked) to other machines in a LAN, an intranet, an extranet, or the Internet. While only a single device is illustrated, the computer system 100 may include any collection of devices that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein. Accordingly, any reference in the disclosure and/or claims to a computer system, computing system, computer device, computing device, control system, control unit, electronic control unit (ECU), processor device, processing circuitry, etc., includes reference to one or more such devices to individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein. For example, control system may include a single control unit or a plurality of control units connected or otherwise communicatively coupled to each other, such that any performed function may be distributed between the control units as desired. Further, such devices may communicate with each other or other devices by various system architectures, such as directly or via a Controller Area Network (CAN) bus, etc.

[94] The computer system 100 may comprise at least one computing device or electronic device capable of including firmware, hardware, and/or executing software instructions to implement the functionality described herein. The computer system 100 may include processing circuitry 102 (e.g., processing circuitry including one or more processor devices or control units), a memory 104, and a system bus 106. The computer system 100 may include at least one computing device having the processing circuitry 102. The system bus 106 provides an interface for system components including, but not limited to, the memory 104 and the processing circuitry 102. The processing circuitry 102 may include any number of hardware components for conducting data or signal processing or for executing computer code stored in memory 104. The processing circuitry 102 may, for example, include a general-purpose processor, an application specific processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA), a circuit containing processing components, a group of distributed processing components, a group of distributed computers configured for processing, or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. The processing circuitry 102 may further include computer executable code that controls operation of the programmable device.

[95] The system bus 106 may be any of several types of bus structures that may further interconnect to a memory bus (with or without a memory controller), a peripheral bus, and/or a local bus using any of a variety of bus architectures. The memory 104 may be one or more devices for storing data and/or computer code for completing or facilitating methods described herein. The memory 104 may include database components, object code components, script components, or other types of information structure for supporting the various activities herein. Any distributed or local memory device may be utilized with the systems and methods of this description. The memory 104 may be communicably connected to the processing circuitry 102 (e.g., via a circuit or any other wired, wireless, or network connection) and may include computer code for executing one or more processes described herein. The memory 104 may include non-volatile memory 108 (e.g., read-only memory (ROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), etc.), and volatile memory 110 (e.g., randomaccess memory (RAM)), or any other medium which can be used to carry or store desired program code in the form of machine-executable instructions or data structures and which can be accessed by a computer or other machine with processing circuitry 102. A basic input/output system (BIOS) 112 may be stored in the non-volatile memory 108 and can include the basic routines that help to transfer information between elements within the computer system 100.

[96] The computer system 100 may further include or be coupled to a non-transitory computer-readable storage medium such as the storage device 114, which may comprise, for example, an internal or external hard disk drive (HDD) (e.g., enhanced integrated drive electronics (EIDE) or serial advanced technology attachment (SATA)), HDD (e.g., EIDE or SATA) for storage, flash memory, or the like. The storage device 114 and other drives associated with computer-readable media and computer-usable media may provide nonvolatile storage of data, data structures, computer-executable instructions, and the like. [97] Computer-code which is hard or soft coded may be provided in the form of one or more modules. The module(s) can be implemented as software and/or hard-coded in circuitry to implement the functionality described herein in whole or in part. The modules may be stored in the storage device 114 and/or in the volatile memory 110, which may include an operating system 116 and/or one or more program modules 118. All or a portion of the examples disclosed herein may be implemented as a computer program 120 stored on a transitory or non-transitory computer-usable or computer-readable storage medium (e.g., single medium or multiple media), such as the storage device 114, which includes complex programming instructions (e.g., complex computer-readable program code) to cause the processing circuitry 102 to carry out actions described herein. Thus, the computer-readable program code of the computer program 120 can comprise software instructions for implementing the functionality of the examples described herein when executed by the processing circuitry 102. In some examples, the storage device 114 may be a computer program product (e.g., readable storage medium) storing the computer program 120 thereon, where at least a portion of a computer program 120 may be loadable (e.g., into a processor) for implementing the functionality of the examples described herein when executed by the processing circuitry 102. The processing circuitry 102 may serve as a controller or control system for the computer system 100 that is to implement the functionality described herein.

[98] The computer system 100 may include an input device interface 122 configured to receive input and selections to be communicated to the computer system 100 when executing instructions, such as from a keyboard, mouse, touch-sensitive surface, etc. Such input devices may be connected to the processing circuitry 102 through the input device interface 122 coupled to the system bus 106 but can be connected through other interfaces, such as a parallel port, an Institute of Electrical and Electronic Engineers (IEEE) 1394 serial port, a Universal Serial Bus (USB) port, an IR interface, and the like. The computer system 100 may include an output device interface 124 configured to forward output, such as to a display, a video display unit (e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT)). The computer system 100 may include a communications interface 126 suitable for communicating with a network as appropriate or desired.

[99] The operational actions described in any of the exemplary aspects herein are described to provide examples and discussion. The actions may be performed by hardware components, may be embodied in machine-executable instructions to cause a processor to perform the actions, or may be performed by a combination of hardware and software. Although a specific order of method actions may be shown or described, the order of the actions may differ. In addition, two or more actions may be performed concurrently or with partial concurrence.

[100] Example 1 : A computer system (100) comprising processing circuitry (102) configured to: retrieve (61) a modeled vehicle tire (3’) from a tire model (10), determine (62) a plurality of grid points (41a-c, 42a-c, 43a-c) of the modeled vehicle tire (3’), said grid points (41a-c, 42a-c, 43a-c) being distributed in a lateral and longitudinal direction of the modeled vehicle tire (3’), retrieve (63) a modeled road (5’) from a road model (20), determine (64) a plurality of projected grid points (51a-c, 52a-c, 53a-c) of the modeled road (5’) by projecting each of the grid points (41a-c, 42a-c, 43a-c) of the modeled vehicle tire (3’) on the modeled road, determine (65) a continuous road surface segment from the projected grid points (51a-c, 52a-c, 53a-c), and compute (66) at least one road-tire interaction parameter (RTIP) from the continuous road surface segment.

[101] Example 2: The computer system of Example 1, wherein the processing circuitry

[102] is further configured to: update the at least one road-tire interaction parameter by continuously repeating retrieve the modelled vehicle tire, determine the plurality of grid points of the modelled vehicle tire, retrieve the modelled road, determine the plurality of projected grid points, determine the continuous road surface segment, and compute at least one road-tire interaction parameter from the continuous road surface segment.

[102] Example 3: The computer system of Example 2, wherein the processing circuitry

[102] is further configured to: adjusting the longitudinal distribution of the plurality of grid points of the modelled vehicle tire when updating the at least one road-tire interaction parameter.

[103] Example 4: The computer system of Example 3, wherein the processing circuitry (102) is further configured to: compress the longitudinal distribution of the plurality of grid points of the modelled vehicle tire when updating the at least one road-tire interaction parameter.

[104] Example 5: The computer system of any of Examples 2-4, wherein the processing circuitry (102) is further configured to: assign at least one of the projected grid points as an actual contact point, and to compute the continuous road surface segment to include the immediately preceding at least one actual contact point. [105] Example 6: The computer system of any of Examples 1-5, wherein the at least one road-tire interaction parameter is a road normal.

[106] Example 7: The computer system of any of Examples 1-6, wherein the processing circuitry (102) is further configured to: determine the plurality of grid points as a nxn grid, preferably n equals 3.

[107] Example 8: The computer system of any of Examples 1-7, wherein the processing circuitry (102) is further configured to: determine the continuous road surface segment by defining a n-dimensional quadratic equation.

[108] Example 9: The computer system of Example 8, wherein the processing circuitry (102) is further configured to: compute the at least one road-tire interaction parameter from at least one partial derivative of the n-dimensional quadratic equation.

[109] Example 10: The computer system of any of Examples 1-9, wherein the processing circuitry (102) is further configured to: determine longitudinally distributed parallel sets of grid points of the modelled vehicle tire, wherein each set of grid points extends laterally.

[110] Example 11 : The computer system of Example 10, wherein the processing circuitry (102) is further configured to: determine a rearward set of grid points at the center of a contact patch of the tire.

[111] Example 12: The computer system of any of Example 10-11, wherein the processing circuitry (102) is further configured to: determine a center set of grid points in front of a contact patch of the tire.

[112] Example 13: The computer system of any of Examples 10-12, wherein the processing circuitry (102) is further configured to: determine a forward set of grid points at the front position of the tire.

[113] Example 14: The computer system of Example 1, wherein the at least one roadtire interaction parameter is a road normal, and wherein the processing circuitry (102) is further configured to: determine the plurality of grid points as a nxn grid, update the at least one road-tire interaction parameter by continuously repeating retrieve the modelled vehicle tire, determine the plurality of grid points of the modelled vehicle tire, retrieve the modelled road, determine the plurality of projected grid points, determine the continuous road surface segment, and compute at least one road-tire interaction parameter from the continuous road surface segment, compressing the longitudinal distribution of the plurality of grid points of the modelled vehicle tire when updating the at least one road-tire interaction parameter, assign at least one of the projected grid points as an actual contact point, and to compute the continuous road surface segment to include the immediately preceding at least one actual contact point, determine the continuous road surface segment by defining a n-dimensional quadratic equation, compute the at least one road-tire interaction parameter from at least one partial derivative of the n-dimensional quadratic equation, determine longitudinally distributed parallel sets of grid points of the modelled vehicle tire, wherein each set of grid points extends laterally, and to determine a rearward set of grid points at the center of a contact patch of the tire, a center set of grid points in front of a contact patch of the tire, and a forward set of grid points at the front position of the tire.

[114] Example 15: A vehicle (1) comprising the computer system (100) of any of Examples 1-14.

[115] Example 16: A computer-implemented method (60), comprising: retrieving (61), by processing circuitry of a computer system, a modeled vehicle tire from a tire model, determining (62), by the processing circuitry, a plurality of grid points of the modeled vehicle tire, said grid points being distributed in a lateral and longitudinal direction of the modeled vehicle tire, retrieving (63), by the processing circuitry, a modeled road from a road model, determining (64), by the processing circuitry, a plurality of projected grid points of the modeled road by projecting each of the grid points of the modeled vehicle tire on the modeled road, determining (65), by the processing circuitry, a continuous road surface segment from the projected grid points, and computing (66), by the processing circuitry, at least one roadtire interaction parameter from the continuous road surface segment.

[116] Example 17: The method of Example 16, wherein the at least one road-tire interaction parameter is a road normal.

[117] Example 18: The method of any of Examples 16-17, wherein: retrieving a modeled vehicle tire, determining a plurality of grid points of the modeled vehicle tire, retrieving a modeled road, determining a plurality of projected grid points of the modeled road, determining a continuous road surface segment, and computing at least one road-tire interaction parameter, is performed for each one of a plurality of wheels of a vehicle.

[118] Example 19: A computer program product comprising program code for performing, when executed by the processing circuitry, the method of any of Examples 16- 18. [119] Example 20: A non-transitory computer-readable storage medium comprising instructions, which when executed by the processing circuitry, cause the processing circuitry to perform the method of any of Examples 16-18.

[120] The terminology used herein is for the purpose of describing particular aspects only and is not intended to be limiting of the disclosure. As used herein, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items. It will be further understood that the terms "comprises," "comprising," "includes," and/or "including" when used herein specify the presence of stated features, integers, actions, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, actions, steps, operations, elements, components, and/or groups thereof.

[121] It will be understood that, although the terms first, second, etc., may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element without departing from the scope of the present disclosure.

[122] Relative terms such as "below" or "above" or "upper" or "lower" or "horizontal" or "vertical" may be used herein to describe a relationship of one element to another element as illustrated in the Figures. It will be understood that these terms and those discussed above are intended to encompass different orientations of the device in addition to the orientation depicted in the Figures. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element, or intervening elements may be present. In contrast, when an element is referred to as being "directly connected" or "directly coupled" to another element, there are no intervening elements present.

[123] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. It will be further understood that terms used herein should be interpreted as having a meaning consistent with their meaning in the context of this specification and the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. [124] It is to be understood that the present disclosure is not limited to the aspects described above and illustrated in the drawings; rather, the skilled person will recognize that many changes and modifications may be made within the scope of the present disclosure and appended claims. In the drawings and specification, there have been disclosed aspects for purposes of illustration only and not for purposes of limitation, the scope of the disclosure being set forth in the following claims.

Claims

Claims

1. A computer system (100) comprising processing circuitry (102) configured to: retrieve (61) a modeled vehicle tire (3’) from a tire model (10), determine (62) a plurality of grid points (41a-c, 42a-c, 43a-c) of the modeled vehicle tire (3’), said grid points (41a-c, 42a-c, 43a-c) being distributed in a lateral and longitudinal direction of the modeled vehicle tire (3’), retrieve (63) a modeled road (5’) from a road model (20), determine (64) a plurality of projected grid points (51a-c, 52a-c, 53a-c) of the modeled road (5’) by projecting each of the grid points (41a-c, 42a-c, 43a-c) of the modeled vehicle tire (3’) on the modeled road, determine (65) a continuous road surface segment from the projected grid points (51a- c, 52a-c, 53a-c), and compute (66) at least one road-tire interaction parameter (RTIP) from the continuous road surface segment.

2. The computer system of claim 1, wherein the processing circuitry (102) is further configured to: update the at least one road-tire interaction parameter by continuously repeating retrieve the modelled vehicle tire, determine the plurality of grid points of the modelled vehicle tire, retrieve the modelled road, determine the plurality of projected grid points, determine the continuous road surface segment, and compute at least one road-tire interaction parameter from the continuous road surface segment.

3. The computer system of claim 2, wherein the processing circuitry (102) is further configured to: adjusting the longitudinal distribution of the plurality of grid points of the modelled vehicle tire when updating the at least one road-tire interaction parameter.

4. The computer system of claim 3, wherein the processing circuitry (102) is further configured to: compress the longitudinal distribution of the plurality of grid points of the modelled vehicle tire when updating the at least one road-tire interaction parameter.

5. The computer system of any of claims 2-4, wherein the processing circuitry (102) is further configured to: assign at least one of the projected grid points as an actual contact point, and to compute the continuous road surface segment to include the immediately preceding at least one actual contact point.

6. The computer system of any of claims 1-5, wherein the at least one road-tire interaction parameter is a road normal.

7. The computer system of any of claims 1-6, wherein the processing circuitry (102) is further configured to: determine the plurality of grid points as a nxn grid, preferably n equals 3.

8. The computer system of any of claims 1-7, wherein the processing circuitry (102) is further configured to: determine the continuous road surface segment by defining a n-dimensional quadratic equation.

9. The computer system of claim 8, wherein the processing circuitry (102) is further configured to: compute the at least one road-tire interaction parameter from at least one partial derivative of the n-dimensional quadratic equation.

10. The computer system of any of claims 1-9, wherein the processing circuitry (102) is further configured to: determine longitudinally distributed parallel sets of grid points of the modelled vehicle tire, wherein each set of grid points extends laterally.

11. The computer system of claim 10, wherein the processing circuitry (102) is further configured to: determine a rearward set of grid points at the center of a contact patch of the tire.

12. The computer system of any of claims 10-11, wherein the processing circuitry (102) is further configured to: determine a center set of grid points in front of a contact patch of the tire.

13. The computer system of any of claims 10-12, wherein the processing circuitry (102) is further configured to: determine a forward set of grid points at the front position of the tire.

14. The computer system of claim 1, wherein the at least one road-tire interaction parameter is a road normal, and wherein the processing circuitry (102) is further configured to: determine the plurality of grid points as a nxn grid, update the at least one road-tire interaction parameter by continuously repeating retrieve the modelled vehicle tire, determine the plurality of grid points of the modelled vehicle tire, retrieve the modelled road, determine the plurality of projected grid points, determine the continuous road surface segment, and compute at least one road-tire interaction parameter from the continuous road surface segment, compressing the longitudinal distribution of the plurality of grid points of the modelled vehicle tire when updating the at least one road-tire interaction parameter, assign at least one of the projected grid points as an actual contact point, and to compute the continuous road surface segment to include the immediately preceding at least one actual contact point, determine the continuous road surface segment by defining a n-dimensional quadratic equation, compute the at least one road-tire interaction parameter from at least one partial derivative of the n-dimensional quadratic equation, determine longitudinally distributed parallel sets of grid points of the modelled vehicle tire, wherein each set of grid points extends laterally, and to determine a rearward set of grid points at the center of a contact patch of the tire, a center set of grid points in front of a contact patch of the tire, and a forward set of grid points at the front position of the tire.

15. A vehicle (1) comprising the computer system (100) of any of claims 1-14.

16. A computer-implemented method (60), comprising: retrieving (61), by processing circuitry of a computer system, a modeled vehicle tire from a tire model, determining (62), by the processing circuitry, a plurality of grid points of the modeled vehicle tire, said grid points being distributed in a lateral and longitudinal direction of the modeled vehicle tire, retrieving (63), by the processing circuitry, a modeled road from a road model, determining (64), by the processing circuitry, a plurality of projected grid points of the modeled road by projecting each of the grid points of the modeled vehicle tire on the modeled road, determining (65), by the processing circuitry, a continuous road surface segment from the projected grid points, and computing (66), by the processing circuitry, at least one road-tire interaction parameter from the continuous road surface segment.

17. The method of claim 16, wherein the at least one road-tire interaction parameter is a road normal.

18. The method of any of claims 16-17, wherein: retrieving a modeled vehicle tire, determining a plurality of grid points of the modeled vehicle tire, retrieving a modeled road, determining a plurality of projected grid points of the modeled road, determining a continuous road surface segment, and computing at least one road-tire interaction parameter, is performed for each one of a plurality of wheels of a vehicle.

19. A computer program product comprising program code for performing, when executed by the processing circuitry, the method of any of claims 16-18.

20. A non-transitory computer-readable storage medium comprising instructions, which when executed by the processing circuitry, cause the processing circuitry to perform the method of any of claims 16-18.